Almgren regularity theorem

In mathematical geometric measure theory, the Almgren regularity theorem, proved by Almgren (1983, 2000), states that the singular set of a mass-minimizing surface has codimension at least 2. Almgren's proof of this was 955 pages long.

References

• Almgren, F. J. (1983), "Q valued functions minimizing Dirichlet's integral and the regularity of area minimizing rectifiable currents up to codimension two", American Mathematical Society. Bulletin. New Series, 8 (2): 327–328, ISSN 0002-9904, MR 684900, doi:10.1090/S0273-0979-1983-15106-6 
• Almgren, Frederick J. Jr. (2000), Taylor, Jean E.; Scheffer, Vladimir, eds., Almgren's big regularity paper. Q-valued functions minimizing Dirichlet's integral and the regularity of area-minimizing rectifiable currents up to codimension 2, World Scientific Monograph Series in Mathematics, 1, River Edge, NJ: World Scientific, ISBN 978-981-02-4108-7, MR 1777737, Zbl 0985.49001 
• Chang, Sheldon X. (1998), "On Almgren's regularity result", The Journal of Geometric Analysis, 8 (5): 703–708, ISSN 1050-6926, MR 1731058, doi:10.1007/BF02922666 
• White, Brian (1998), "The mathematics of F. J. Almgren, Jr", The Journal of Geometric Analysis, 8 (5): 681–702, ISSN 1050-6926, MR 1731057, doi:10.1007/BF02922665